Urgh. I am getting a little desperate here, this puzzle has me badly confused. I have but a single red party left to hunt down, and it is sitting in what appears to be (to my poor confused mind) an unsolvable riddle.

Am I missing something really obvious?

P
O
S
S
I
B
L
E

S
P
O
I
L
E
R
!

Where the unique party sits, two sliding walls point to it, and there is nowhere to get it to move to so I can shift those walls to get at it. I have tried teleporting around in the hopes that I could hop in there, but no luck. I think I have stepped on every square that is available to me, and tried every combination of the switches, including one that seems too far away to make much of an effect. The fourth switch also does not give the same message that the other three do.

bbb}_b
bFbb_b
bR{}_b
b^_b_b

bbb_{b
bFbb_b
bR{_{b
b^_b_b

These are the two configurations I can get, the top allows me to get at the third switch but I cannot get anything new from this. Just more grinding cut short. The b are walls, the brackets are sliding walls, the R is a unique party and the F is a freeborn party waiting around in there. The _ are clear spaces.

I hope that this is:
a) enough information for someone to be able to give me a nudge, and
b) not so much information that I get dropped from these forums.